LCM of 310 and 315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 310 and 315 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 19530 as output. Here you can check the answer for Find the LCM of 310 and 315.
What is LCM of 310 and 315
Given Numbers are 310, 315
We can find the LCM of 310, 315 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 310 and 315
Multiples of 310 =310,620,930,1240,1550,1860,2170,2480,2790,3100,3410,3720,4030,4340,4650,4960,5270,
Multiples of 315 =315,630,945,1260,1575,1890,2205,2520,2835,3150,3465,3780,4095,4410,4725,5040,5355,
Now, get the least common multiple of 310, 315 which is 19530
So, the LCM of 310, 315 is 19530.
Least Common Multiple (LCM) of 310 and 315 with the help of Prime Factorisation
One method for determining the LCM of 310 and 315 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 310's prime factorization:
| 2 | 310 |
| 5 | 155 |
| 31 | 31 |
| 1 |
Prime factors of 310 are 2, 5,31.
310 = 21×51×311
And this is 315's prime factorization:
| 3 | 315 |
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 315 are 3, 5,7.
315 = 32×51×71
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2, 5,31, 3,7
.21×32×51×71×311 = 19530
This shows that the LCM of 310 and 315 is 19530.
How to Calculate the LCM of 310 and 315 Using Common Multiples
The first step in determining the Least Common Multiple of 310 and 315 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 310 and 315:
Lets look at the first ten multiples of these numbers, 310 and 315:
310,620,930,1240,1550,1860,2170,2480,2790,5270 are the first ten multiples of 310.
315,630,945,1260,1575,1890,2205,2520,2835,5355 are the first ten multiples of 315.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 310 and 315, for example, are 3720, 5270, and 5040. 19530 is the least common multiple since it is the smallest.
310 and 315 have an LCM of 19530.
Least Common Multiple of 310 and 315 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 310 and 315, than apply into the LCM equation.
GCF(310,315) = 5
LCM(310,315) = ( 310 × 315) / 5
LCM(310,315) = 97650 / 5
LCM(310,315) = 19530
Related Least Common Multiples of 310
Related Least Common Multiples of 315
Frequently Asked Questions on LCM of 310 and 315
1. What is the LCM of 310 and 315?
The LCM of 310 and 315 is 19530.
2. How to find the lowest common multiple of 310 and 315?
To find the lowest common multiple of 310 and 315, we have to get the multip;es of both numbers and identify the least common multiple in them which is 19530.
3. What are the Factors of 310?
Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.
4. What are the Factors of 315?
Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.
5. How to Find the LCM of 310 and 315?Answer:
Least Common Multiple of 310 and 315 = 19530
Step 1: Find the prime factorization of 310
310 = 2 x 5 x 31
Step 2: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 19530 = 2 x 3 x 3 x 5 x 7 x 31
Step 4: Therefore, the least common multiple of 310 and 315 is 19530.